Largest Eigenvalue Distribution of Noncircularly Symmetric Wishart-Type Matrices With Application to Hoyt-Faded MIMO Communications

Abstract

This paper is concerned with the largest eigenvalue of the Wishart-type random matrix $\mathbf {{W}}=\mathbf {{X}}\mathbf {{X}}^\dagger$ (or $\mathbf {{W}}=\mathbf {{X}}^\dagger \mathbf {{X}}$ ), where $\mathbf {{X}}$ is a complex Gaussian matrix with unequal variances in the real and imaginary parts of its entries, i.e., $\mathbf {X}$ belongs to the noncircularly symmetric Gaussian subclass. By establishing a novel connection with the well-known complex Wishart ensemble, we here derive exact and asymptotic expressions for the largest eigenvalue distribution of $\mathbf {{W}}$ , which provide new insights on the effect of the real-imaginary variance imbalance of the entries of $\mathbf {X}$ . These new results are then leveraged to analyze the outage performance of multiantenna systems with maximal ratio combining subject to Nakagami- $q$ (Hoyt) fading.